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Semiparametric error-correction models for cointegration with trends: Pseudo-Gaussian and optimal rank-based tests of the cointegration rank

Marc Hallin (), Ramon van den Akker and Bas J.M. Werker

Journal of Econometrics, 2016, vol. 190, issue 1, 46-61

Abstract: This paper provides pseudo-Gaussian and locally optimal rank-based tests for the cointegration rank in linear cointegrated error-correction models with common trends and i.i.d. elliptical innovations. The proposed tests are asymptotically distribution-free, hence their validity does not depend on the actual distribution of the innovations. The proposed rank-based tests depend on the choice of scores, associated with a reference density that can freely be chosen. Under appropriate choices they are achieving the semiparametric efficiency bounds; when based on Gaussian scores, they moreover uniformly dominate their pseudo-Gaussian counterparts. Simulations show that the asymptotic analysis provides an accurate approximation to finite-sample behavior. The theoretical results are based on a complete picture of the asymptotic statistical structure of the model under consideration.

Keywords: Cointegration model; Cointegration rank; Elliptical densities; Error-correction model; Lagrange multiplier test; Local asymptotic Brownian functional; Local asymptotic mixed normality; Local asymptotic normality; Multivariate ranks; Quasi-likelihood procedures; Rank tests; Semiparametric efficiency (search for similar items in EconPapers)
JEL-codes: C14 C32 (search for similar items in EconPapers)
Date: 2016
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